There are two potential solutions to this problem, but both have caveats, the first because of your use of Flex and a standalone projector, the second because it is a mitigator, not a complete solution.
Hardware Acceleration
When publishing your file, you can attempt to have Flash utilize hardware acceleration to alleviate the vertical refresh issue you are running into that is causing tearing. Sadly, Flex Builder 3 is incapable of enabling this setting at the SWF (projector) level (Link to bug). This has yet to be resolved and has been pushed from 4.0 to 4.1 to 4.x... If and when it is resolved, it will likely be a compiler argument in the project settings of Flash Builder 4.
You may be able to determine if this solution works for you by outputting your projector as a standard SWF and embedding it on an HTML document with the wmode set to "direct" or "gpu". Sadly, if it does (it should), you can't use it right now anyway. If you have Flash Builder 4, certain projects are capable of making round trips between FB4 and Flash Professional CS5, though I am not sure what the criteria for that is (my current AIR project has all the project modification menu options grayed out). If you do manage to get your project into Flash, you can enable hardware acceleration in the Publish Settings of the project (File->Publish Settings->Flash tab->Hardware Acceleration option in CS5).
This method is almost a certain solution for your problem, though it has two issues, one already highlighted above, and (for people publishing for the web) that by utilizing direct or GPU rendering on a webpage, you are unable to layer any DOM elements on top of flash.
direct: This mode tries to use the fastest path to screen, or direct path if you will. In most cases it will ignore whatever the browser would want to do to have things like overlapping HTML menus or such work. A typical use case for this mode is video playback. On Windows this mode is using DirectDraw or Direct3D on Vista, on OSX and Linux we are using OpenGL. Fidelity should not be affected when you use this mode.
gpu: This is fully fledged compositing (+some extras) using some functionality of the graphics card. Think of it being similar to what OSX and Vista do for their desktop managers, the content of windows (in flash language that means movie clips) is still rendered using software, but the result is composited using hardware. When possible we also scale video natively in the card. More and more parts of our software rasterizer might move to the GPU over the next few Flash Player versions, this is just a start. On Windows this mode uses Direct3D, on OSX and Linux we are using OpenGL.
*Source
Direct is the ideal option for this situation, as you can actually have performance degredation with "gpu" as well as visual differences from graphics card to graphics card.
Lower your framerate
The Flash player will continue to play video at its native refresh rate independent of the rest of your project as long as you keep the framerate at or above approximately 2FPS (though I suggest 5FPS minimum). You won't want to run that low for this example, but you are able to lower the framerate of the entire scene without impacting video performance. The closer your framerate is to the screen refresh rate, the more apt you are to actually create the tearing effect unless you are able to absolutely sync with the monitor's refresh rate, which you probably cannot do without the above... Hardware Acceleration.
This problem has existed in the Flash Player for as long as it has been able to move objects horizontally. What happens is that Flash updates a buffered snapshot of the running animation at the same time that the screen is refreshing. If the buffered snapshot changes partway through a screen refresh, you get a tear. This is why lowering the framerate actually reduces the amount of tearing, you are refreshing the buffer less frequently.